The figure shows a network of five capacitors connected to a 20 V battery. Calculate the charge acquired by each 10 $$\mu$$F capacitor.

A parallel plate capacitor is filled by a dielectric whose relative permittivity varies with the applied voltage (U) as $$\epsilon=2 U$$. A similar capacitor with no dielectric is charged to $$U_0=78 \mathrm{~V}$$. It is then connected to the uncharged capacitor with the dielectric. Find the final voltage on the capacitors.

A capacitor of capacity $$2 ~\mu \mathrm{F}$$ is charged upto a potential $$14 \mathrm{~V}$$ and then connected in parallel to an uncharged capacitor of capacity $$5 ~\mu \mathrm{F}$$. The final potential difference across each capacitor will be

A dielectric of dielectric constant $$K$$ is introduced such that half of its area of a capacitor of capacitance $$C$$ is occupied by it. The new capacity is